Erdős Similarity Problem via Bi-Lipschitz Embedding-Reference-Cited by-同舟云学术

Erdős Similarity Problem via Bi-Lipschitz Embedding

Published:2024-08-02 Issue:17 Volume:2024 Page:12327-12342
ISSN:1073-7928
Container-title:International Mathematics Research Notices
language:en
Short-container-title:

Author:

Feng De-Jun¹,Lai Chun-Kit²,Xiong Ying³

Affiliation:

1. Department of Mathematics, The Chinese University of Hong Kong , Shatin , Hong Kong

2. Department of Mathematics, San Francisco State University , 1600 Holloway Avenue, San Francisco, CA 94132 , USA

3. Department of Mathematics, South China University of Technology , Guangzhou 510641, Guangdong , People’s Republic of China

Abstract

Abstract The Erdős similarity conjecture asserted that an infinite set of real numbers cannot be affinely embedded into every measurable set of positive Lebesgue measure. The problem is still open, in particular for all fast decaying sequences. In this paper, we relax the problem to the bi-Lipschitz embedding and obtain some sharp criteria about the bi-Lipschitz Erdős similarity problem for strictly decreasing sequences.

Funder

General Research Fund

Hong Kong Research Grant Council

Chinese University of Hong Kong

NSFC

Publisher

Oxford University Press (OUP)

Link

https://academic.oup.com/imrn/article-pdf/2024/17/12327/59013844/rnae167.pdf

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